Related papers: Equivariant Spherical Deconvolution: Learning Spar…
The goal of self-supervised visual representation learning is to learn strong, transferable image representations, with the majority of research focusing on object or scene level. On the other hand, representation learning at part level has…
Diffusion-weighted Magnetic Resonance Imaging (dMRI) is increasingly used to study the fetal brain in utero. An important computation enabled by dMRI is streamline tractography, which has unique applications such as tract-specific analysis…
Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…
Our work expands the use of capsule networks to the task of object segmentation for the first time in the literature. This is made possible via the introduction of locally-constrained routing and transformation matrix sharing, which reduces…
Relationships in scientific data, such as the numerical and spatial distribution relations of features in univariate data, the scalar-value combinations' relations in multivariate data, and the association of volumes in time-varying and…
We present a convex formulation of dictionary learning for sparse signal decomposition. Convexity is obtained by replacing the usual explicit upper bound on the dictionary size by a convex rank-reducing term similar to the trace norm. In…
We propose a novel approach for performing convolution of signals on curved surfaces and show its utility in a variety of geometric deep learning applications. Key to our construction is the notion of directional functions defined on the…
The discovery of the theory of compressed sensing brought the realisation that many inverse problems can be solved even when measurements are "incomplete". This is particularly interesting in magnetic resonance imaging (MRI), where long…
We propose a multi-shell sampling grid and develop corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The transform is exact in the…
In domains such as molecular and protein generation, physical systems exhibit inherent symmetries that are critical to model. Two main strategies have emerged for learning invariant distributions: designing equivariant network architectures…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
Diffusion MRI (dMRI) is a widely used imaging modality, but requires long scanning times to acquire high resolution datasets. By leveraging the unique geometry present within this domain, we present a novel approach to dMRI angular…
Diffusion magnetic resonance imaging (dMRI) enables non-invasive investigation of tissue microstructure. The Standard Model (SM) of white matter aims to disentangle dMRI signal contributions from intra- and extra-axonal water compartments.…
X-ray diffraction is ideal for probing sub-surface state during complex or rapid thermomechanical loading of crystalline materials. However, challenges arise as the size of diffraction volumes increases due to spatial broadening and…
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…
Tractography parcellation classifies streamlines reconstructed from diffusion MRI into anatomically defined fiber tracts for clinical and research applications. However, clinical scans often have incomplete fields of view (FOV) where brain…
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those…
White matter structures composed of myelinated axons in the living human brain are primarily studied by diffusion-weighted MRI (dMRI). These long-range projections are typically characterized in a two-step process: dMRI is used to estimate…
Removing the aberrations introduced by the Point Spread Function (PSF) is a fundamental aspect of astronomical image processing. The presence of noise in observed images makes deconvolution a nontrivial task that necessitates the use of…
A new method for improving the resolution of astronomical images is presented. It is based on the principle that sampled data cannot be fully deconvolved without violating the sampling theorem. Thus, the sampled image should not be…